test/aoj/icpc/2402.test.cpp

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Last update: 2023-06-05 10:52:20+09:00
Problem: https://onlinejudge.u-aizu.ac.jp/problems/2402

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Code

// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2402
// verification-helper: ERROR 0.000001

#include "src/real-geometry/angle/degree-to-radian.hpp"
#include "src/real-geometry/class/point.hpp"
#include "src/real-geometry/class/segment.hpp"
#include "src/real-geometry/distance/distance-ss.hpp"
#include "src/real-geometry/mapping/rotate.hpp"
#include "src/real-geometry/utility/io-set.hpp"

#include <iostream>
#include <algorithm>

using namespace geometry;

using R = long double;
const R inf = 1e8;

R star_distance(int a, int b, const std::vector< segments< R > > &stars) {
  R res = inf;

  for (auto &seg_a : stars[a]) {
    for (auto &seg_b : stars[b]) {
      res = std::min(res, distance_ss(seg_a, seg_b));
    }
  }

  return res;
}

using Graph = std::vector< std::vector< R > >;

void solve(int n, int m, int l) {
  std::vector< segments< R > > stars(n);
  Graph G(n, std::vector< R >(n));

  for (auto &star : stars) {
    point< R > p;
    R a, r;
    std::cin >> p >> a >> r;

    point< R > v(0, r);
    points< R > ps;
    for (int i = 0; i < 6; i++) {
      ps.emplace_back(v);
      v = rotate<R>(degree_to_radian<R>(144), v);
    }

    for (auto &pt : ps) {
      pt = rotate(degree_to_radian(a), pt);
      pt += p;
    }

    for (int i = 0; i < 5; i++) {
      segment< R > s(ps[i], ps[i + 1]);
      star.emplace_back(s);
    }
  }

  for (int v = 0; v < n; v++) {
    for (int u = 0; u < n; u++) {
      G[v][u] = star_distance(v, u, stars);
    }
  }

  for (int k = 0; k < n; k++) {
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        G[i][j] = std::min(G[i][j], G[i][k] + G[k][j]);
      }
    }
  }

  std::cout << G[m][l] << std::endl;
}

int main() {
  IoSetup(20);
  int n, m, l;

  while (std::cin >> n >> m >> l, n) {
    solve(n, m - 1, l - 1);
  }
}

#line 1 "test/aoj/icpc/2402.test.cpp"
// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2402
// verification-helper: ERROR 0.000001

#line 2 "src/real-geometry/angle/degree-to-radian.hpp"

#line 2 "src/real-geometry/common/const/pi.hpp"

#line 2 "src/real-geometry/common/float-alias.hpp"

namespace geometry {

  using f80 = long double;
  using f64 = double;

}
#line 4 "src/real-geometry/common/const/pi.hpp"

#include <cmath>

namespace geometry {

  static f80 pi() {
    static const f80 PI = acosl(-1); // no need `std::`. (?)
    return PI;
  }

}
#line 4 "src/real-geometry/angle/degree-to-radian.hpp"

namespace geometry {

  // warning: to use degree_to_radian<R>(deg) 
  //          if type of deg is `int`
  template< typename R >
  R degree_to_radian(R deg) {
    return deg * pi() / 180.0;
  }

}
#line 2 "src/real-geometry/class/point.hpp"

#line 2 "src/real-geometry/class/vector.hpp"

#include <complex>
#include <iostream>

namespace geometry {

  template< typename R >
  class vec2d : public std::complex< R > {
    using complex = std::complex< R >;

   public:
    using complex::complex;

    vec2d(const complex &c): complex::complex(c) {}

    const R x() const { return this->real(); }
    const R y() const { return this->imag(); }

    friend vec2d operator*(const vec2d &v, const R &k) {
      return vec2d(v.x() * k, v.y() * k);
    }

    friend vec2d operator*(const R &k, const vec2d &v) {
      return vec2d(v.x() * k, v.y() * k);
    }

    friend std::istream &operator>>(std::istream &is, vec2d &v) {
      R x, y;
      is >> x >> y;
      v = vec2d(x, y);
      return is;
    }
 
  };

}
#line 4 "src/real-geometry/class/point.hpp"

#include <vector>

namespace geometry {

  template< typename R >
  using point = vec2d<R>;

  template< typename R >
  using points = std::vector< point< R > >;

}
#line 2 "src/real-geometry/class/segment.hpp"

#line 2 "src/real-geometry/utility/equals/vector.hpp"

#line 2 "src/real-geometry/utility/equals/real-number.hpp"

#line 2 "src/real-geometry/utility/sign.hpp"

#line 2 "src/real-geometry/common/const/eps.hpp"

#line 4 "src/real-geometry/common/const/eps.hpp"

namespace geometry {

  inline static f80 &eps() {
    static f80 EPS = 1e-10;
    return EPS;
  }

  void set_eps(f80 EPS) {
    eps() = EPS;
  }

}
#line 2 "src/real-geometry/numbers/sign.hpp"

#line 2 "src/real-geometry/common/int-alias.hpp"

namespace geometry {

  using i32 = int;
  using i64 = long long;

}
#line 4 "src/real-geometry/numbers/sign.hpp"

namespace geometry::number::sign {

  constexpr i32 PLUS  = +1;
  constexpr i32 ZERO  =  0;
  constexpr i32 MINUS = -1;

}
#line 5 "src/real-geometry/utility/sign.hpp"

namespace geometry {

  using namespace geometry::number::sign;

  template< typename R >
  inline int sign(R r) {
    if (r < -eps()) return MINUS;
    if (r > +eps()) return PLUS;
    return ZERO;
  }

}
#line 4 "src/real-geometry/utility/equals/real-number.hpp"

namespace geometry {

  template< typename R >
  bool equals(R a, R b) {
    return sign(a - b) == 0;
  }

}
#line 5 "src/real-geometry/utility/equals/vector.hpp"

namespace geometry {

  template< typename R >
  bool equals(const vec2d<R> &a, const vec2d<R> &b) {
    return equals(a.x(), b.x()) and equals(a.y(), b.y());
  }

}
#line 5 "src/real-geometry/class/segment.hpp"

#include <cassert>
#line 8 "src/real-geometry/class/segment.hpp"

namespace geometry {

  template< typename R >
  class segment {
   public:
    point<R> a, b;

    segment() = default;
    segment(point<R> a, point<R> b) : a(a), b(b) {
      assert(not equals(a, b));
    }

  };

  template< typename R >
  using segments = std::vector< segment<R> >;

}
#line 2 "src/real-geometry/distance/distance-ss.hpp"

#line 2 "src/real-geometry/distance/distance-sp.hpp"

#line 2 "src/real-geometry/mapping/projection.hpp"

#line 2 "src/real-geometry/class/line.hpp"

#line 5 "src/real-geometry/class/line.hpp"

#line 8 "src/real-geometry/class/line.hpp"

namespace geometry {

  template< typename R >
  class line {
    using P = point<R>;

   public:
    P a, b;

    line() = default;
    line(P a, P b) : a(a), b(b) {
      assert(not equals(a, b));
    }

  };

  template< typename R >
  using lines = std::vector< line<R> >;

}
#line 2 "src/real-geometry/operation/inner-product.hpp"

#line 4 "src/real-geometry/operation/inner-product.hpp"

namespace geometry {

  template< typename R >
  R inner_product(const vec2d<R> &a, const vec2d<R> &b) {
    return a.x() * b.x() + a.y() * b.y();
  }

}
#line 6 "src/real-geometry/mapping/projection.hpp"

#line 8 "src/real-geometry/mapping/projection.hpp"

namespace geometry {

  template< typename R >
  point<R> projection(const line<R> &l, const point<R> &p) {
    R t = inner_product<R>(p - l.a, l.a - l.b) / std::norm(l.a - l.b);
    return l.a + (l.a - l.b) * t;
  }

}
#line 2 "src/real-geometry/operation/ccw.hpp"

#line 2 "src/real-geometry/numbers/ccw.hpp"

namespace geometry::number::ccw {

  constexpr int COUNTER_CLOCKWISE = +1;
  constexpr int CLOCKWISE         = -1;
  constexpr int ONLINE_BACK       = +2; // c-a-b
  constexpr int ONLINE_FRONT      = -2; // a-b-c
  constexpr int ON_SEGMENT        =  0; // a-c-b

}
#line 2 "src/real-geometry/operation/cross-product.hpp"

#line 4 "src/real-geometry/operation/cross-product.hpp"

namespace geometry {

  template< typename R >
  R cross_product(const vec2d<R> &a, const vec2d<R> &b) {
    return a.x() * b.y() - a.y() * b.x();
  }

}
#line 8 "src/real-geometry/operation/ccw.hpp"

namespace geometry {

  using namespace geometry::number::ccw;

  template< typename R >
  int ccw(const point<R> &a, point<R> b, point<R> c) {
    b = b - a, c = c - a;
    if (sign(cross_product(b, c)) == +1) return COUNTER_CLOCKWISE;
    if (sign(cross_product(b, c)) == -1) return CLOCKWISE;
    if (sign(inner_product(b, c)) == -1) return ONLINE_BACK;
    if (std::norm(b) < std::norm(c)) return ONLINE_FRONT;
    return ON_SEGMENT;
  }
}
#line 7 "src/real-geometry/distance/distance-sp.hpp"

#line 9 "src/real-geometry/distance/distance-sp.hpp"
#include <algorithm>

namespace geometry {

  template< typename R >
  R distance_sp(const segment<R> &s, const point<R> &p) {
    point<R> pr = projection({s.a, s.b}, p);
    if (ccw(s.a, s.b, pr) == 0) return std::abs(pr - p);
    return std::min(std::abs(s.a - p), std::abs(s.b - p));
  }

}
#line 2 "src/real-geometry/position/intersect-ss.hpp"

#line 5 "src/real-geometry/position/intersect-ss.hpp"

namespace geometry {

  template< typename R >
  bool intersect_ss(const segment<R> &s1, const segment<R> &s2) {
    return ccw(s1.a, s1.b, s2.a) * ccw(s1.a, s1.b, s2.b) <= 0 and
           ccw(s2.a, s2.b, s1.a) * ccw(s2.a, s2.b, s1.b) <= 0;
  }

}
#line 6 "src/real-geometry/distance/distance-ss.hpp"

#line 8 "src/real-geometry/distance/distance-ss.hpp"

namespace geometry {

  template< typename R >
  R distance_ss(const segment<R> &s1, const segment<R> &s2) {
    if (intersect_ss(s1, s2)) return 0;
    R r1 = distance_sp(s1, s2.a);
    R r2 = distance_sp(s1, s2.b);
    R r3 = distance_sp(s2, s1.a);
    R r4 = distance_sp(s2, s1.b);
    return std::min({r1, r2, r3, r4});
  }

}
#line 2 "src/real-geometry/mapping/rotate.hpp"

#line 4 "src/real-geometry/mapping/rotate.hpp"

#line 6 "src/real-geometry/mapping/rotate.hpp"

namespace geometry {

  template< typename R >
  vec2d<R> rotate(const R theta, const vec2d<R> &v) {
    return {std::cos(theta) * v.x() + std::sin(-theta) * v.y(),
            std::sin(theta) * v.x() + std::cos(-theta) * v.y()};
  }

}
#line 2 "src/real-geometry/utility/io-set.hpp"

#include <iomanip>

namespace geometry {

  class IoSetup {
    using u32 = unsigned int;

    void set(std::ostream &os, u32 precision) {
      os << std::fixed << std::setprecision(precision);
    }

   public:
    IoSetup(u32 precision = 15) {
      std::cin.tie(0);
      std::ios::sync_with_stdio(0);

      set(std::cout, precision);
      set(std::cerr, precision);
    }
  } iosetup;

}
#line 10 "test/aoj/icpc/2402.test.cpp"

#line 13 "test/aoj/icpc/2402.test.cpp"

using namespace geometry;

using R = long double;
const R inf = 1e8;

R star_distance(int a, int b, const std::vector< segments< R > > &stars) {
  R res = inf;

  for (auto &seg_a : stars[a]) {
    for (auto &seg_b : stars[b]) {
      res = std::min(res, distance_ss(seg_a, seg_b));
    }
  }

  return res;
}

using Graph = std::vector< std::vector< R > >;

void solve(int n, int m, int l) {
  std::vector< segments< R > > stars(n);
  Graph G(n, std::vector< R >(n));

  for (auto &star : stars) {
    point< R > p;
    R a, r;
    std::cin >> p >> a >> r;

    point< R > v(0, r);
    points< R > ps;
    for (int i = 0; i < 6; i++) {
      ps.emplace_back(v);
      v = rotate<R>(degree_to_radian<R>(144), v);
    }

    for (auto &pt : ps) {
      pt = rotate(degree_to_radian(a), pt);
      pt += p;
    }

    for (int i = 0; i < 5; i++) {
      segment< R > s(ps[i], ps[i + 1]);
      star.emplace_back(s);
    }
  }

  for (int v = 0; v < n; v++) {
    for (int u = 0; u < n; u++) {
      G[v][u] = star_distance(v, u, stars);
    }
  }

  for (int k = 0; k < n; k++) {
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        G[i][j] = std::min(G[i][j], G[i][k] + G[k][j]);
      }
    }
  }

  std::cout << G[m][l] << std::endl;
}

int main() {
  IoSetup(20);
  int n, m, l;

  while (std::cin >> n >> m >> l, n) {
    solve(n, m - 1, l - 1);
  }
}